Efficient equilibrium-based stress recovery for isogeometric laminated curved structures

TL;DR

This paper presents an efficient stress recovery method for laminated curved structures using Isogeometric Analysis, enabling accurate out-of-plane stress computation from coarse displacement data without iterative procedures.

Contribution

It introduces a novel equilibrium-based post-processing step for IGA that accurately recovers out-of-plane stresses in laminated structures, reducing computational cost compared to layerwise techniques.

Findings

Accurate out-of-plane stress recovery from coarse displacement solutions.

Effective for structures with high radius-to-thickness ratios.

Reduces computational cost compared to traditional layerwise methods.

Abstract

This work focuses on an efficient stress recovery procedure for laminated composite curved structures, which relies on Isogeometric Analysis (IGA) and equilibrium. Using a single element through the thickness in combination with a calibrated layerwise integration rule or a homogenized approach, the 3D solid isogeometric modeling grants an inexpensive and accurate approximation in terms of displacements (and their derivatives) and in-plane stresses, while through-the-thickness stress components are poorly approximated. Applying a further post-processing step, an accurate out-of-plane stress state is also recovered, even from a coarse displacement solution. This is based on a direct integration of the equilibrium equations in strong form, involving high order derivatives of the displacement field. Such a continuity requirement is fully granted by IGA shape function properties. The post-processing step is locally applied, which grants that no additional coupled terms appear in the equilibrium, allowing for a direct reconstruction without the need to further iterate to resolve the out-of-balance momentum equation. Several numerical results show the good performance of this approach particularly for composite stacks with significant radius-to-thickness ratio and number of plies. In particular, in the latter case, where a layerwise technique employing a number of degrees of freedom directly proportional to the number of plies would be much more computationally demanding, the proposed method can be regarded as a very appealing alternative choice.